Effective isoscalar nucleon-nucleon interactions at 500 MeV

The 500 MeV effective nucleon-nucleon isoscalar interaction is investigated through nonrelativistic folding model analysis of $\overrightarrow{p}$+nucleus elastic scattering data. Three empirical interactions are deduced. The first, obtained from a relativistic-Schrödinger-equation-equivalent form of a phenomenological Dirac optical potential, contains terms which are dependent on the square of the nuclear matter density. A modified version of this interaction is then obtained, in which the density dependence is made explicit. Finally, an optical potential is deduced which depends linearly on the density, resulting in a density-independent nucleon-nucleon effective interaction. Nuclear size information inferred from calculations using these effective interactions is found to be in reasonable agreement with theoretical expectations. The relative merits of each of these three forms of the interaction are discussed.